Mounting band 21fb-fjp22
 

There is a type of material that is around the tube where the mounting band sits what is an alternate material that can be used since the old stuff is dry rotted and cannot be used again.

If you are talking about the padding material and not the strap it's self then it was either coark, foam rubber, or layers of friction tape.... Anything similar that will provide some grip and mild padding should work.

There's always Duct Tape. Ask any criminal. :D

Should this friction tape be the cloth type or will vinyl tape work. Or would duct tape work as well.

The original friction tape on sets that had it (Predictas come to mind but many other TVs had it) was cloth...Same thing as the old cloth style electrical tape that people used in the 1920s-1950s. Ace still sells it.

Ok good thanks

Is there any rule to adhere to when tightening the steel strap on the 21 inch round tube.

Removable mounting bands (as opposed to the permanent compression bands that were permanently attached to some much later tube types) should be tightened only enough to hold the tube in place.
Edit: the mount should be designed and perhaps have cushioning so that excess force is not applied to the tube even though screws are firmly tightened. If the tape you applied is the only cushioning, then the caution about overtightening applies.